Robust label attribution for real-time bidding

Most of the display advertising inventory is sold through real-time auctions. The participants of these auctions are typically bidders (Google, Criteo, RTB House, Trade Desk for instance) who participate on behalf of advertisers. In order to estimate the value of each display opportunity, they usually train advanced machine learning algorithms using historical data. In the labeled training set, the inputs are vectors of features representing each display opportunity and the labels are the generated rewards. In practice, the rewards are given by the advertiser and are tied to whether or not a particular user converts. Consequently, the rewards are aggregated at the user level and never observed at the display level. A fundamental task that has, to the best of our knowledge, been overlooked is to account for this mismatch and split, or attribute, the rewards at the right granularity level before training a learning algorithm. We call this the label attribution problem. In this paper, we develop an approach to the label attribution problem which is both theoretically justified and practical. We dub our solution the robust label attribution because it satisfies several desirable properties, including distributional robustness. Moreover, we develop a fixed point algorithm that allows for large scale implementation and showcase our solution using a large scale publicly available dataset from Criteo, a large Demand Side Platform.